Chemical Kinetics - Molecularity and Order

  • Molecularity and order are important concepts in chemical kinetics
  • They help us understand the rate at which reactions occur

Molecularity

  • Molecularity refers to the number of molecules or ions involved in an elementary step of a reaction
  • It is determined by the balanced chemical equation for the reaction

Molecularity Examples

  1. 2NO2 ⟶ 2NO + O2
    • This reaction is a bimolecular reaction because it involves two molecules of NO2
  1. N2O5 ⟶ 2NO2 + 1/2O2
    • This reaction is also a bimolecular reaction because it involves two molecules of N2O5

Order

  • Order refers to the power to which the concentration of a reactant is raised in the rate equation
  • It is determined experimentally

Reaction Order Examples

  1. Rate = k[A]
    • This is a first-order reaction because the concentration of A is raised to the power of 1
  1. Rate = k[A][B]^2
    • This is a second-order reaction because the concentration of A is raised to the power of 1 and the concentration of B is raised to the power of 2

Determining Order Experimentally

  • Order can be determined by measuring the reaction rate at different concentrations of the reactants
  • Several experiments are performed to obtain a set of data points
  • The data is then analyzed to determine the order of the reaction

Rate Law Expression

  • The rate law expression is an equation that relates the rate of a reaction with the concentrations of the reactants
  • It is obtained by experimental measurements

Rate Law Expression Example

  • For the reaction: 2NO + O2 ⟶ 2NO2
  • The rate law expression is: Rate = k[NO]^2[O2]

Rate Constant (k)

  • The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentrations of the reactants
  • It is specific to a particular reaction at a given temperature

Rate Constant Example

  • For the reaction: 2NO + O2 ⟶ 2NO2
  • The rate law expression is: Rate = k[NO]^2[O2]
  • The rate constant (k) can be determined experimentally ``markdown

Slide 11

  • Rate Constants and Temperature
    • The rate constant (k) is dependent on temperature
    • As the temperature increases, the rate constant generally increases
    • The relationship between rate constant and temperature is given by the Arrhenius equation
  • Arrhenius Equation
    • The Arrhenius equation relates the rate constant with the activation energy (Ea) and the temperature (T)
    • It is expressed as: k = Ae^(-Ea/RT)
    • A is the pre-exponential factor or the frequency factor, R is the gas constant (8.314 J/mol•K), and T is the temperature in Kelvin
  • Activation Energy
    • Activation energy (Ea) is the energy required for a chemical reaction to occur
    • It represents the energy barrier that the reactants must overcome before they can form products
    • A higher activation energy results in a slower reaction rate
  • Collision Theory
    • The collision theory explains how particles must collide in a favorable manner in order for a reaction to occur
    • For a reaction to take place:
      • The particles must collide with sufficient energy (greater than the activation energy)
      • The particles must collide with the correct orientation
    • Increasing temperature increases the number of collisions with sufficient energy, thus increasing the reaction rate
  • Exponential Increase with Temperature
    • The Arrhenius equation shows that the rate constant increases exponentially with temperature
    • Even small changes in temperature can have a significant impact on the reaction rate ``

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Slide 12

  • Temperature Dependence of Reaction Rate
    • The rate of a reaction generally doubles for every 10-degree Celsius increase in temperature (known as the “10-degree rule”)
    • This relationship can be quantified using the concept of reaction rate constant and the Arrhenius equation
  • Activation Energy and Reaction Rate
    • Activation energy affects the reaction rate by determining how fast the reactant molecules can transform into products
    • A higher activation energy requires more energy input, resulting in slower reaction rates
    • Lower activation energy allows molecules to convert into products more easily, leading to faster reaction rates
  • Energy Profile Diagram
    • An energy profile diagram represents the energy changes that occur during a chemical reaction
    • It includes reactants, products, activation energy, and the overall change in energy
    • The activation energy is the energy difference between the reactants and the highest energy point (transition state) in the reaction pathway
  • Catalysts
    • Catalysts are substances that increase the reaction rate by providing an alternative reaction pathway with lower activation energy
    • They increase the rate of both the forward and reverse reactions, but do not take part in the overall reaction
    • Catalysts are not consumed during the reaction and can be reused
  • Effect of Catalysts on Activation Energy
    • Catalysts lower the activation energy by providing an alternative reaction pathway with a lower energy barrier
    • This allows more reactant molecules to possess sufficient energy to overcome the barrier, increasing the reaction rate ``

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Slide 13

  • Rate-Determining Step
    • The rate-determining step is the slowest step in a reaction mechanism
    • It determines the overall rate of the reaction
    • The rate law is determined by the coefficients of the reactants involved in the rate-determining step
  • Reaction Mechanism
    • A reaction mechanism describes the series of steps by which a reaction occurs
    • Each step in the mechanism has its own rate and may involve different reactants or intermediates
    • The overall reaction is the sum of the individual steps in the mechanism
  • Elementary Reactions
    • Elementary reactions are individual steps in a reaction mechanism that involve a small number of reactant molecules
    • They are often bimolecular or unimolecular reactions
    • The rate law for an elementary reaction can be directly determined from its stoichiometry
  • Rate Determination
    • The rate-determining step determines the overall rate of the reaction
    • Reactions are often multi-step processes, but the rate of the overall reaction is determined by the slowest step
  • Rate Laws and Mechanisms
    • The rate law for a reaction is determined by the slowest elementary step in the reaction mechanism
    • By studying the reaction mechanism, we can understand how reactants are converted to products and determine the rate law for the overall reaction ``

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Slide 14

  • Reaction Intermediates
    • Reaction intermediates are species that are formed in one step of a reaction mechanism and consumed in a subsequent step
    • They are neither reactants nor products in the overall reaction
    • Reaction intermediates are often short-lived and difficult to detect
  • Catalysts and Reaction Mechanism
    • Catalysts participate in the reaction mechanism by forming intermediate complexes with reactant molecules
    • They lower the activation energy for the rate-determining step, increasing the reaction rate
    • Catalysts are regenerated in subsequent steps of the mechanism
  • Rate Law and Rate-Determining Step
    • The slowest step in the mechanism determines the rate law for the overall reaction
    • The coefficients of the reactants in the rate-determining step correspond to the exponents in the rate law
  • Rate Law and Reaction Order
    • The reaction order is determined by the sum of the exponents of the reactant concentrations in the rate law
    • The reaction order usually does not correspond to the stoichiometric coefficients in the balanced equation
  • Rate Law and Rate Constant
    • The rate constant for the rate-determining step is included in the rate law equation
    • It represents the proportionality constant between the rate of the reaction and the concentrations of the reactants ``

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Slide 15

  • Half-Life of a Reaction
    • The half-life of a reaction is the time it takes for the concentration of a reactant to decrease by half
    • It is influenced by the reaction order
    • The half-life can be calculated using the rate constant and the initial concentration of the reactant
  • Half-Life and Reaction Order
    • For a first-order reaction, the half-life is independent of the initial concentration
    • For a second-order reaction, the half-life is dependent on the initial concentration
    • The half-life can provide valuable information about the reaction rate and the reaction order
  • Determining Reaction Order from Experimental Data
    • By analyzing the concentration data of reactants at different time intervals, the reaction order can be determined
    • Plotting the natural logarithm of the reactant concentration versus time yields a straight line for first-order reactions
    • Plotting the inverse of the reactant concentration versus time yields a straight line for second-order reactions
  • Reaction Order and Rate Constants
    • The reaction order affects the rate constant of a reaction
    • The rate constant is specific to a particular reaction at a given temperature and is independent of reactant concentrations
  • Integrated Rate Laws
    • Integrated rate laws express the relationship between the concentration of a reactant and time for a specific reaction order
    • They are derived from the rate law expression and can be used to determine the concentration of reactants at any given time ``

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Slide 16

  • Zero-Order Reactions
    • In a zero-order reaction, the rate of the reaction is independent of the concentration of the reactants
    • This means that the reaction proceeds at a constant rate over time
    • The rate law for a zero-order reaction is: Rate = k
    • The concentration of the reactants does not appear in the rate law equation
  • First-Order Reactions
    • In a first-order reaction, the rate of the reaction is directly proportional to the concentration of a single reactant
    • The rate law for a first-order reaction is: Rate = k[A]
    • The half-life of a first-order reaction is constant and independent of the initial concentration
  • Second-Order Reactions
    • In a second-order reaction, the rate of the reaction is proportional to the square of the concentration of a single reactant or the product of the concentrations of two reactants
    • The rate law for a second-order reaction is: Rate = k[A]^2 or Rate = k[A][B]
    • The half-life of a second-order reaction is dependent on the initial concentration of the reactant
  • Determining Reaction Order from Experimental Data
    • By analyzing the concentration data of reactants at different time intervals, the reaction order can be determined
    • Different reaction orders exhibit characteristic patterns on concentration-time plots
    • Integration of the rate law equation can also help determine the reaction order
  • Determining Rate Law from Experimental Data
    • By conducting experiments at different reactant concentrations, the rate law can be determined
    • The rate law can be obtained by comparing the initial rates of reaction at different concentrations of reactants ``

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Slide 17

  • Collision Theory - Reactant Concentration
    • The rate of a reaction is proportional to the concentration of the reactants
    • Increasing the concentration of the reactants increases the number of collisions between reactant molecules, leading to a higher reaction rate
    • This is because a greater number of collisions results in more successful collisions that lead to product formation
  • Collision Theory - Temperature
    • Increasing the temperature increases the average kinetic energy of the reactant molecules
    • This increases the frequency and the energy of collisions between the reactant molecules
    • Higher energy collisions are more likely to surpass the activation energy barrier, resulting in a higher reaction rate
  • Collision Theory - Surface Area
    • Increasing the surface area of a solid reactant increases the number of exposed particles available for collisions
    • This leads to an increased frequency of collisions and therefore a higher reaction rate
  • Collision Theory - Catalysts
    • Catalysts provide an alternative reaction pathway with lower activation energy
    • They increase the likelihood of successful collisions between reactant molecules, resulting in a higher reaction rate
    • Catalysts do not affect the equilibrium position or the overall ∆H of the reaction
  • Collision Theory - Orientation and Steric Effects
    • For a collision to be successful, the reactant molecules must collide with the proper orientation and geometry
    • Steric hindrance can occur if bulky groups prevent the reactant molecules from proper orientation
    • Proper orientation and steric factors play an important role in determining the rate of a reaction ``

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Slide 18

  • Reaction Rate and Concentration
    • The rate of a reaction depends on the concentration of the reactants
    • Higher concentrations result in more frequent collisions, leading to a higher reaction rate
    • The dependence of reaction rate on reactant concentrations is expressed in the rate law equation
  • Rate Determining Step and Overall Reaction
    • The rate-determining step is the slowest step in a reaction mechanism
    • It determines the overall rate of the reaction
    • The rate law is based on the stoichiometry of the reactants involved in the rate-determining step
  • Reaction Order and Rate Law
    • The reaction order is determined by the sum of the exponents of the reactant concentrations in the rate law equation
    • The reaction order does not necessarily correspond to the stoichiometric coefficients in the balanced chemical equation
  • Determining Reaction Order from Experimental Data
    • The reaction order can be determined by measuring the reaction rate at different concentrations of the reactants
    • Experimental data is analyzed to create a graph of concentration versus time or concentration versus rate
  • Integrated Rate Laws and Half-Life
    • Integrated rate laws are mathematical expressions that relate the concentration of a reactant to time for a specific reaction order
    • The half-life of a reaction is the time it takes for the reactant concentration to decrease to half of its initial value
    • The half-life can be determined using the rate constant and the initial concentration of the reactant ``

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Slide 19

  • Temperature and Reaction Rate
    • Increasing the temperature increases the kinetic energy of the reactant molecules
    • This leads to more frequent and energetic collisions, resulting in a higher reaction rate
    • The relationship between temperature and reaction rate is described by the Arrhenius equation
  • Arrhenius Equation
    • The Arrhenius equation relates the rate constant to the activation energy and temperature
    • It is expressed as: k = Ae^(-Ea/RT)
    • A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin
  • Activation Energy and Reaction Rate
    • Activation energy is the minimum energy required for a reaction to occur
    • A reaction with a higher activation energy proceeds at a slower rate compared to a reaction with a lower activation energy
    • Catalysts lower the activation energy and increase the reaction rate
  • Reaction Mechanism and Rate Determination
    • Reaction mechanisms describe the sequence of steps by which a reaction occurs
    • The slowest step, known as the rate-determining step, determines the overall reaction rate
    • The rate law is based on the stoichiometry of the reactants involved in the rate-determining step
  • Effect of Catalysts on Activation Energy
    • Catalysts provide an alternative reaction pathway with lower activation energy
    • This lowers the energy barrier for the reaction, allowing more reactant molecules to form products, and increases the reaction rate ``

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Slide 20

  • Rate Constants and Temperature
    • The rate constant (k) is dependent on temperature
    • As the temperature increases, the rate constant generally increases
    • The relationship between rate constant and temperature is given by the Arrhenius equation
  • Arrhenius Equation
    • The Arrhenius equation relates the rate constant with the activation energy (Ea) and the temperature (T)
    • It is expressed as: k = Ae^(-Ea/RT)
    • A is the pre-exponential factor or the frequency factor, R is the gas constant (8.314 J/mol•K), and T is the temperature in Kelvin
  • Activation Energy
    • Activation energy (Ea) is the energy required for a chemical reaction to occur
    • It represents the energy barrier that the reactants must overcome before they can form products
    • A higher activation energy results in a slower reaction rate
  • Collision Theory
    • The collision theory explains how particles must collide in a favorable manner in order for a reaction to occur
    • For a reaction to take place:
      • The particles must collide with sufficient energy (greater than the activation energy)
      • The particles must collide with the correct orientation
    • Increasing temperature increases the number of collisions with sufficient energy, thus increasing the reaction rate
  • Exponential Increase with Temperature
    • The Arrhenius equation shows that the rate constant increases exponentially with temperature
    • Even small changes in temperature can have a significant impact on the reaction rate markdown

Slide 21

  • Rate Laws and Experimental Data
    • Rate laws can be determined experimentally by measuring the reaction rate at different concentrations of reactants
    • Data is collected and analyzed to determine the dependence of rate on reactant concentrations
    • The order of the reaction can be determined from the experimental data
  • Determining Order from Concentration-Time Plots
    • For a first-order reaction, the natural logarithm of the reactant concentration decreases linearly with time
    • For a second-order reaction, the inverse of the reactant concentration increases linearly with time
    • Analyzing the concentration-time plot can help determine the reaction order
  • Determining Order from Initial Rate Data
    • The initial rate of reaction is measured at different concentrations of reactants
    • By comparing the initial rates, the reaction order can be determined
    • The order is determined by the change in reaction rate with respect to changes in reactant concentrations
  • Determining Rate Constants from Experimental Data
    • Once the reaction order is determined, the rate constant can be calculated
    • The rate constant is determined from the experimental data by rearranging the rate law equation and substituting the initial concentrations
    • The rate constant is specific to a particular reaction at a given temperature
  • Effect of Temperature on Reaction Rate
    • Increasing temperature generally increases the reaction rate